Temperature-adjusted analyte determination for biosensor systems

ABSTRACT

A biosensor system determines analyte concentration from an output signal generated by an oxidation/reduction reaction of the analyte. The biosensor system adjusts a correlation for determining analyte concentrations from output signals at one temperature to determining analyte concentrations from output signals at other temperatures. The temperature-adjusted correlation between analyte concentrations and output signals at a reference temperature may be used to determine analyte concentrations from output signals at a sample temperature.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/413,028 entitled “Temperature-Adjusted Analyte Determination forBiosensor Systems” filed Mar. 6, 2012, now U.S. Pat. No. 8,445,290,which was a continuation of U.S. application Ser. No. 12/839,643entitled “Temperature-Adjusted Analyte Determination for BiosensorSystem” filed Jul. 20, 2010, now U.S. Pat. No. 8,148,162, which was acontinuation of U.S. application Ser. No. 12/187,743 entitled“Temperature-Adjusted Analyte Determination for Biosensor System” filedAug. 7, 2008, now U.S. Pat. No. 7,781,222, which was a continuation ofPCT/US2007/004712 entitled “Temperature-Adjusted Analyte Determinationfor Biosensor Systems” filed Feb. 23, 2007, which was published inEnglish and claimed the benefit of U.S. Provisional Application No.60/776,986 entitled “Temperature-Adjusted Analyte Determination forBiosensor Systems” as filed on Feb. 27, 2006, each of which isincorporated herein by reference.

BACKGROUND

Biosensor systems usually provide an analysis of one or more analytes inbiological fluids. The analysis typically includes a quantitativedetermination of the analyte in the biological fluid. The analysis isuseful in the diagnosis and treatment of physiological abnormalities.For example, the determination of the glucose level in blood isimportant to diabetic individuals who frequently check their bloodglucose level to regulate diet and/or medication. For other individuals,the monitoring of uric acid, lactate, cholesterol, bilirubin, and thelike may be important.

Biosensor systems may be implemented using bench-top, portable, andother measuring devices. The portable devices may be hand-held andusually include a measuring device and a sensor strip. Typically, asample of a biological fluid is introduced to the sensor strip, which isdisposed in the measuring device for analysis. Biosensor systems may bedesigned to analyze one or more analytes and may use different volumesof biological fluids. Some biosensor systems may analyze a single dropof whole blood (WB), such as from 1-15 microliters (μL) in volume.

Biosensor systems usually measure an output signal to determine theanalyte concentration in a sample of the biological fluid. The outputsignal is generated from an oxidation/reduction or redox reaction of theanalyte. An enzyme or similar species may be added to the sample toenhance the redox reaction. The output signal may be an electric signal,light, or light converted to an electric signal. A biosensor system maygenerate the output signal using an optical sensor system or anelectrochemical sensor system.

In optical systems, the analyte concentration is determined by measuringlight that has interacted with a light-identifiable species, such as theanalyte or a reaction or product formed from a chemical indicatorreacting with the analyte redox reaction. An incident excitation beamfrom a light source is directed toward the sample. Thelight-identifiable species absorbs or shifts the wavelength of a portionof the incident beam, thus altering the wavelength or reducing theintensity of the incident beam. A detector collects and measures theattenuated or wavelength-altered incident beam, which is the outputsignal. In other optical systems, the chemical indicator fluoresces oremits light in response to the analyte redox reaction when illuminatedby the excitation beam. A detector collects and measures the light,which is the output signal.

In electrochemical systems, the analyte concentration is determined bymeasuring an electrical signal, such as a current or potential.Typically, the analyte undergoes the redox reaction when an excitationsignal is applied to the sample. The excitation signal usually is anelectrical signal, such as a current or potential. The redox reactiongenerates an output signal in response to the excitation signal. Theoutput signal usually is an electrical signal, such as a current orpotential, which may be measured and correlated with the concentrationof the analyte.

In electrochemical systems, the measuring device usually has electricalcontacts that connect with electrical conductors in the sensor strip.The electrical connectors are connected by the conductors to electrodesthat extend into the sample of the biological fluid. The measuringdevice applies the excitation signal through the electrical contacts tothe electrical conductors, which convey the excitation signal into thesample through the electrodes. The redox reaction of the analytegenerates an output signal in response to the excitation signal. Themeasuring device determines the analyte concentration in response to theoutput signal. Examples of portable measuring devices include theAscensia Breeze® and Elite® meters of Bayer Corporation; the Precision®biosensors available from Abbott in Abbott Park, Ill.; Accucheck®biosensors available from Roche in Indianapolis, Ind.; and OneTouchUltra® biosensors available from Lifescan in Milpitas, Calif. Examplesof bench-top measuring devices include the BAS 100B Analyzer availablefrom BAS Instruments in West Lafayette, Ind.; the CH Instruments'Electrochemical Workstation available from CH Instruments in Austin,Tex.; the Cypress Electrochemical Workstation available from CypressSystems in Lawrence, Kans.; and the EG&G Electrochemical Instrumentavailable from Princeton Research Instruments in Princeton, N.J.

Sensor strips may include reagents that react with the analyte in thesample of biological fluid. The reagents include an ionizing agent forfacilitating the redox of the analyte, as well as any mediators or othersubstances that assist in transferring electrons between the analyte andthe conductor. The ionizing agent may be an analyte specific enzyme,such as glucose oxidase or glucose dehydrogenase, to catalyze theoxidation of glucose in a WB sample. The reagents may include a binderthat holds the enzyme and mediator together. In optical systems, thereagents include the chemical indicator along with another enzyme orlike species to enhance the reaction of the chemical indicator with theanalyte or products of the analyte redox reaction.

Most biosensor systems use correlation or calibration equations todetermine the analyte concentration in a sample of a biological fluid.Correlation equations represent the relationship between output signalsand analyte concentrations. From each correlation equation, an analyteconcentration may be calculated for a particular output signal. Thecorrelation equations are dependent on the temperature of the sample.The output signal for a particular analyte concentration may change dueto the effect of temperature on the redox reaction of the analyte,enzyme kinetics, diffusion, and the like. A correlation equation may beneeded for each possible sample temperature in order to calculate theanalyte concentration from an output signal at a particular sampletemperature.

To reduce the number of correlation equations used in the sampleanalysis, many biosensor systems attempt to provide analyteconcentrations using one or more correlation equations for a particularreference temperature. The analyte concentration at a sample temperatureusually is compensated for the difference between the sample temperatureand the reference temperature to provide an analyte concentration at thereference temperature.

Some biosensor systems compensate for temperature by changing the outputsignal prior to calculating the analyte concentration from a correlationequation. The output signal usually is multiplied by a temperaturecorrection coefficient or the like. The temperature-corrected outputsignal is used to determine the analyte concentration. Biosensor systemsusing a temperature-corrected output signal are described in U.S. Pat.Nos. 4,750,496 and 6,576,117.

Other biosensor systems compensate for temperature by changing theanalyte concentration calculated by the correlation equation. Theanalyte concentration calculated from the correlation equation usuallyundergoes a temperature correction procedure to provide atemperature-corrected analyte concentration. Biosensor systems using atemperature-corrected analyte concentration are described in U.S. Pat.Nos. 5,366,609; 5,508,171; and 6,391,645.

Additional biosensor systems compensate for temperature by changing theoutput signal prior to calculating the analyte concentration from acorrelation equation and/or by changing the analyte concentrationcalculated by the correlation equation. Biosensor systems using atemperature-corrected output signal and/or a temperature-correctedanalyte concentration are described in U.S. Pat. Nos. 4,431,004 and5,395,504.

While these temperature compensation methods balance various advantagesand disadvantages, none are ideal. These methods may not fullyincorporate various effects of different sample temperatures on theredox reaction of the analyte, the enzyme and mediator kinetics, anddiffusion. These methods may not adequately address effects of differentanalyte concentrations on enzyme kinetics and diffusion at differentsample temperatures. These methods also may not adequately addresseffects of different analyte concentrations on the redox reaction atdifferent sample temperatures. In addition, the changes to the outputsignal and/or the calculated analyte concentration may introduce ormagnify errors related to the determination of the analyte concentrationfrom the output signal.

Accordingly, there is an ongoing need for improved biosensor systems,especially those that may provide increasingly accurate and preciseanalyte concentrations at a reference temperature. The systems, devices,and methods of the present invention overcome at least one of thedisadvantages associated with conventional biosensor systems.

SUMMARY

The present invention provides a biosensor system that determines theanalyte concentration in a sample of a biological fluid from an outputsignal generated by a redox reaction of the analyte. The biosensorsystem adjusts a correlation between analyte concentrations and outputsignals at a reference temperature to determine analyte concentrationsfrom output signals at other temperatures. The biosensor system uses thetemperature-adjusted correlation to determine the analyte concentrationfrom an output signal at a sample temperature.

In a method for determining an analyte concentration in a sample of abiological fluid, the sample temperature is determined. An output signalis generated in response to a redox reaction of an analyte in thesample. A correlation between analyte concentrations and output signalsat a reference temperature is adjusted in response to temperature. Theanalyte concentration is determined from the temperature-adjustedcorrelation and the output signal at the sample temperature.

In a method for adjusting a correlation between analyte concentrationsand output signals at a reference temperature in response totemperature, the correlations between analyte concentrations and outputsignals are determined for a reference temperature and at least oneother temperature. The normalized temperature functions of slope andintercept are developed for the correlation of the referencetemperature. The correlation of the reference temperature is adjusted inresponse to the normalized temperature functions of slope and intercept.

A biosensor for determining an analyte concentration in a biologicalfluid includes a measuring device and sensor strip. The measuring devicehas a processor connected to a sensor interface and a temperaturesensor. The sensor strip has a sample interface on a base. The sampleinterface is adjacent to a reservoir formed by the base. The processoradjusts a correlation between analyte concentrations and output signalsat a reference temperature in response to a sample temperature from thetemperature sensor. The processor determines an analyte concentrationfrom the temperature-adjusted correlation in response to an outputsignal from the sample interface.

The following definitions are included to provide a clearer and moreconsistent understanding of the specification and claims.

“Analyte” is defined as one or more substances present in a sample. Ananalysis determines the presence and/or concentration of the analytepresent in the sample.

“Sample” is defined as a composition that may contain an unknown amountof the analyte. Typically, a sample for electrochemical analysis is inliquid form, and preferably the sample is an aqueous mixture. A samplemay be a biological sample, such as blood, urine, or saliva. A samplealso may be a derivative of a biological sample, such as an extract, adilution, a filtrate, or a reconstituted precipitate.

“Conductor” is defined as an electrically conductive substance thatremains stationary during an electrochemical analysis.

“Accuracy” is defined as how close the amount of analyte measured by asensor system corresponds to the true amount of analyte in the sample.Accuracy may be expressed in terms of the bias of the sensor system'sanalyte reading in comparison to a reference analyte reading. Largerbias values reflect less accuracy.

“Precision” is defined as how close multiple analyte measurements arefor the same sample. Precision may be expressed in terms of the spreador variance among multiple measurements.

“Redox reaction” is defined as a chemical reaction between two speciesinvolving the transfer of at least one electron from a first species toa second species. Thus, a redox reaction includes an oxidation and areduction. The oxidation half-cell of the reaction involves the loss ofat least one electron by the first species, while the reductionhalf-cell involves the addition of at least one electron to the secondspecies. The ionic charge of a species that is oxidized is made morepositive by an amount equal to the number of electrons removed.Likewise, the ionic charge of a species that is reduced is made lesspositive by an amount equal to the number of electrons gained.

“Mediator” is defined as a substance that may be oxidized or reduced andthat may transfer one or more electrons. A mediator is a reagent in anelectrochemical analysis and is not the analyte of interest, butprovides for the indirect measurement of the analyte. In a simplisticsystem, the mediator undergoes a redox reaction in response to theoxidation or reduction of the analyte. The oxidized or reduced mediatorthen undergoes the opposite reaction at the working electrode of thesensor strip and is regenerated to its original oxidation number.

“Binder” is defined as a material that provides physical support andcontainment to the reagents while having chemical compatibility with thereagents.

“Steady-state” is defined as when the change of a signal with respect toits independent input variable (time, etc.) is substantially constant,such as within ±10 or ±5%.

“Transient point” is defined as the value of a signal obtained as afunction of time when an increasing rate of diffusion transitions into arelatively constant rate of diffusion. Before the transient point, thesignal is rapidly changing with time. Similarly, after the transientpoint, the rate of signal decay becomes relatively constant, thusreflecting the relatively constant rate of diffusion.

“Handheld device” is defined as a device that may be held in a humanhand and is portable. An example of a handheld device is the measuringdevice accompanying Ascensia® Elite Blood Glucose Monitoring System,available from Bayer HealthCare, LLC, Elkhart, Ind.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention. Moreover, in the figures, likereferenced numerals designate corresponding parts throughout thedifferent views.

FIG. 1 represents a method for determining an analyte concentration in asample of a biological fluid.

FIG. 2 represents a method for adjusting a correlation between analyteconcentrations and output signals at a reference temperature in responseto a sample temperature.

FIG. 3 is a graph illustrating correlations between analyteconcentrations and output signals.

FIG. 4 is a graph illustrating normalized slopes as a function oftemperature for correlations between glucose concentrations in wholeblood and current for an assay time of 7 seconds.

FIG. 5 is a graph illustrating normalized intercepts as a function oftemperature for correlations between glucose concentrations in wholeblood and current for an assay time of 7 seconds.

FIG. 6 is a graph illustrating the normalized slopes as a function oftemperature for correlations between glucose concentrations in wholeblood and current for several assay times.

FIG. 7 is a graph illustrating the normalized intercepts as a functionof temperature for correlations between glucose concentrations in wholeblood and current for several assay times.

FIG. 8 is a graph illustrating the bias from a reference temperature ofcalculated glucose concentrations without any adjustment fortemperature.

FIG. 9 is a graph illustrating the bias from a reference temperature ofcalculated glucose concentrations with adjustment for temperature.

FIG. 10 is a graph illustrating the temperature function of current froma glucose sensor with normalized slope and intercept.

FIG. 11 is a graph illustrating the temperature coefficient function forthe normalized current of FIG. 10 in relation to temperature.

FIG. 12 depicts a schematic representation of a biosensor thatdetermines an analyte concentration in a sample of a biological fluid.

DETAILED DESCRIPTION

A biosensor system that determines an analyte in a sample of abiological fluid is described. The biosensor system determines theanalyte concentration from an output signal generated by anoxidation/reduction or redox reaction of the analyte. The system adjustsa correlation equation for determining analyte concentrations fromoutput signals at one temperature to determining analyte concentrationsfrom output signals at other temperatures, such as the sampletemperature. The temperature-adjusted correlations improve the accuracyand precision of the biosensor system in determining the analyteconcentration of the sample. The biosensor system may determine analyteconcentrations from output signals at a sample temperature using atemperature-adjusted correlation equation for a reference temperature.The correlation equations between analyte concentrations and outputsignals may be represented graphically, mathematically, a combinationthereof, or the like. The correlation equations may be represented by aprogram number (PNA) table, another look-up table, or the like. Thebiosensor system may be utilized to determine analyte concentrationssuch as glucose, uric acid, lactate, cholesterol, bilirubin, and thelike.

FIG. 1 represents a method for determining an analyte concentration in asample of a biological fluid. In 102, the sample temperature isdetermined. In 104, an output signal is generated in response to anoxidation/reduction reaction of the analyte in the sample. In 106, acorrelation between analyte concentrations and output signals at areference temperature is adjusted in response to temperature. In 108,the analyte concentration is determined from the temperature-adjustedcorrelation and the output signal at the sample temperature. In 110, theanalyte concentration is displayed and may be stored for futurereference.

In 102 of FIG. 1, the sample temperature may be determined using varioustechniques. The sample temperature may be measured using a thermister,thermometer, or other temperature sensing device. The sample temperaturemay be calculated from the output signal of an electrochemical reactionin the sample. The sample temperature may be assumed to be the same orsimilar to a measurement of the ambient temperature or the temperatureof a device implementing the biosensor system. Other techniques may beused to determine the sample temperature.

In 104 of FIG. 1, an output signal is generated in response to anoxidation/reduction or redox reaction of an analyte in the sample. Theoutput signal may be generated using an optical sensor system, anelectrochemical sensor system, or the like.

Optical sensor systems generally measure the amount of light absorbed orgenerated by the reaction of a chemical indicator with the analyte redoxreaction. An enzyme may be included with the chemical indicator toenhance the reaction kinetics. The output signal or light from anoptical system may be converted into an electrical signal such ascurrent or potential.

In light-absorption optical systems, the chemical indicator produces areaction product that absorbs light. A chemical indicator such astetrazolium along with an enzyme such as diaphorase may be used.Tetrazolium usually forms formazan (a chromagen) in response to theredox reaction of the analyte. An incident excitation beam from a lightsource is directed toward the sample. The light source may be a laser, alight emitting diode, or the like. The incident beam may have awavelength selected for absorption by the reaction product. As theincident beam passes through the sample, the reaction product absorbs aportion of the incident beam, thus attenuating or reducing the intensityof the incident beam. The incident beam may be reflected back from ortransmitted through the sample to a detector. The detector collects andmeasures the attenuated incident beam (output signal). The amount oflight attenuated by the reaction product is an indication of the analyteconcentration in the sample.

In light-generated optical systems, the chemical detector fluoresces oremits light in response to the analyte redox reaction. A detectorcollects and measures the generated light (output signal). The amount oflight produced by the chemical indicator is an indication of the analyteconcentration in the sample.

Electrochemical systems apply an input signal to the sample of thebiological fluid. The input signal may be a potential or current and maybe constant, variable, or a combination thereof such as when an ACsignal is applied with a DC signal offset. The input signal may beapplied as a single pulse or in multiple pulses, sequences, or cycles.The analyte undergoes a redox reaction when the input signal is appliedto the sample. An enzyme or similar species may be used to enhance theredox reaction of the analyte. A mediator may be used to maintain theoxidation state of the enzyme. The redox reaction generates the outputsignal that may be measured constantly or periodically during transientand/or steady-state output. Various electrochemical processes may beused such as amperometry, coulometry, voltammetry, or the like. Gatedamperometry and gated voltammetry also may be used.

In amperometry, a potential or voltage is applied to a sample of thebiological fluid. The redox reaction of the analyte generates a currentin response to the potential. The current is measured over time toquantify the analyte in the sample. Amperometry generally measures therate at which the analyte is oxidized or reduced to determine theanalyte concentration in the sample. Biosensor systems using amperometryare described in U.S. Pat. Nos. 5,620,579; 5,653,863; 6,153,069; and6,413,411.

In coulometry, a potential is applied to a sample of the biologicalfluid to exhaustively oxidize or reduce the analyte within the sample.The potential generates a current that is integrated over the time ofoxidation/reduction to produce an electrical charge representing theanalyte concentration. Coulometry generally captures the total amount ofanalyte within the sample. A biosensor system using coulometry for wholeblood glucose measurement is described in U.S. Pat. No. 6,120,676.

In voltammetry, a varying potential is applied to a sample of biologicalfluid. The redox reaction of the analyte generates current in responseto the applied potential. The current is measured over time to quantifythe analyte in the sample. Voltammetry generally measures the rate atwhich the analyte is oxidized or reduced to determine the analyteconcentration in the sample. Additional information about voltammetrymay be found in “Electrochemical Methods: Fundamentals and Applications”by A. J. Bard and L. R. Faulkner, 1980.

In gated amperometry and gated voltammetry, pulsed excitations are usedas described in U.S. Provisional Patent Application Nos. 60/700,787,filed Jul. 20, 2005, and 60/722,584, filed Sep. 30, 2005, respectively,which are incorporated by reference.

In 106 of FIG. 1, a correlation between analyte concentrations andoutput signals at a reference temperature is adjusted in response totemperature. The correlation may be represented by a correlation orcalibration equation that calculates analyte concentrations from outputsignals at the reference temperature. The correlation equation for thereference temperature is adjusted to calculate analyte concentrations inresponse to output signals at other temperatures such as the sampletemperature. The correlation equation may be for a reference temperatureof 25° C. Correlation equations for other reference temperatures may beused.

The correlation equation may be implemented to manipulate the outputsignal for determination of the analyte concentration. The correlationequation also may be implemented as a program number assignment (PNA)table of the slope and intercept for the correlation equation, anotherlook-up table, or the like for comparison with the electrical outputsignal to determine the analyte concentration.

The effect of temperature on the correlation or calibration equations isresponsive to the behavior of diffusion and enzymatic reactions duringthe redox reaction. For example, temperature affects the oxidation anddiffusion of glucose in a sample of whole blood. In addition,temperature affects the diffusion of optically active molecules.

The correlation equations may be linear or near linear, and may bedescribed by a second order polynomial. In a general form, thecorrelation equation can be represented as follows:OS=d _(n) *A ^(n) +d _(n-1) *A ^(n-1) + . . . +d ₂ *A ² +d ₁ *A+d₀  (1).

Where A is the analyte concentration, OS is the output signal, andcoefficients d_(n), d_(n-1), d₂, d₁, and d₀ describe a temperaturedependent weighing factor for each term of the biosensor response.

The correlation equation may be described by the reverse expression,where the analyte concentration is expressed as a function of the outputsignal. This reduces the need to solve an n^(th) order equation in orderto find the analyte concentration. Thus, the correlation equation foranalyte concentration may be represented as follows:A=c _(n) *OS ^(n) +c _(n-1) *OS ^(n-1) + . . . +c ₂ *OS ² +c ₁ *OS+c₀  (2).

Where c_(n), c_(n-1), c₂, c₁, and c₀ are coefficients that describe atemperature dependent weighing factor for each term of the biosensorresponse. The analyte concentration, A, may be glucose in a sample ofwhole blood. The output signal may be the current or potential of anelectrochemical system, the absorbance or %-transmission of an opticalsystem, or the like.

The correlation equation may be represented by a 2^(nd) order responsebetween analyte concentration and output signals as follows:A=c ₂ *OS ² +c ₁ *OS+c ₀  (3).

The correlation equation may be represented by a linear response betweenanalyte concentration and output signals as follows:A _(R) =c ₁ *OS _(T) +c ₀ =OS _(T) /S _(T) +Int _(T) /S _(T)  (4).

Where c₁=1/S_(T), c₀=Int_(T)/S_(T), and where A_(R) is the analyteconcentration at a reference temperature, OS_(T) is the output signal,S_(T) is the product of a slope at the reference temperature and anormalized temperature function of the slope, and Int_(T) is the productof an intercept at the reference temperature and a normalizedtemperature function of the intercept.

Equation (4) may be rewritten to express the output signal in responseto the analyte concentration as follows:OS _(T) =S _(T) *A _(R) +Int _(T)  (5).

Where OS_(T) is the output signal at another temperature such as thesample temperature, A_(R) is the analyte concentration at the referencetemperature, S_(T) can be expressed as a product of a constant and anormalized temperature function of the slope, and Int_(T) can beexpressed as a product of a constant and a normalized temperaturefunction of the intercept.

Equation (5) indicates that the output signal, OS_(T), is a function oftemperature in terms of the temperature effect on slope, S_(T), andintercept, Int_(T), under the analyte concentration, A_(R). The slope,S_(T), and intercept, Int_(T), adjust the slope and intercept of acorrelation equation at a reference temperature using normalizedtemperature functions of the slope and intercept. Thetemperature-adjusted slope and intercept of the correlation for thereference temperature may be used with an output signal at anothertemperature, such as the sample temperature, to calculate an analyteconcentration.

Accordingly, the correlation equation (5) may be rewritten to calculateanalyte concentrations using the temperature-adjusted slope andintercept of the correlation for the reference temperature and outputsignals at another temperature, as follows:

$\begin{matrix}{A_{R} = {\frac{{OS}_{T} - {Int}_{T}}{S_{T}}.}} & (6)\end{matrix}$

Where A_(R) is the analyte concentration at the reference temperature,OS_(T) is the output signal at the other temperature, Int_(T) is theintercept of the correlation for the reference temperature adjusted by anormalized temperature function for the intercept in response to theother temperature, and S_(T) is the slope of the correlation for thereference temperature adjusted by a normalized temperature function forthe slope in response to the other temperature.

The slope of the correlation for the reference temperature is adjustedin response to the sample temperature, as follows:S _(T) =S _(R) *f(T)  (7).

Where S_(R) is the slope of the correlation for the referencetemperature and f(T) is a temperature function that adjusts the slopefor the sample temperature.

The temperature function of slope, f(T), adjusts the slope of thecorrelation for the reference temperature to the slope of a correlationfor another temperature. The temperature-adjusted slope may be used tocalculate the analyte or glucose concentration using an output signal orcurrent generated at the other temperature. To develop the temperaturefunction of slope, f(T), the slopes of correlations for othertemperatures are normalized to the slope of the correlation for thereference temperature. The normalized slope of a correlation for aparticular temperature is a unitless coefficient that adjusts the slopeof the correlation for the reference temperature to the slope of thecorrelation for the particular temperature. The normalized slope of thecorrelation for the reference temperature is essentially one, indicatingthere is little or no adjustment to the slope of the correlation for thereference temperature. The normalized slopes are analyzed graphicallyand/or mathematically such as with a regression analysis to develop thetemperature function of slope, f(T). Another normalization method may beused to develop the temperature function.

The temperature function of slope, f(T), may be a second orderpolynomial such as follows:f(T)=a ₂ T ² +a ₁ T+a ₀  (8).

Where T is the sample temperature and a₂, a₁, and a₀ are coefficients ofa regression analysis representing the normalized slopes. Whilerepresented as a polynomial, the temperature function of slope, f(T),may be represented as a constant, an exponential, trigonometric, orother function, a combination thereof, and the like.

The intercept of the correlation for the reference temperature isadjusted in response to the sample temperature, as follows:Int _(T) =Int _(T) *g(T)  (9).

Where Int_(R) is the intercept of the correlation for the referencetemperature and g(T) is a temperature function that adjusts theintercept for the sample temperature.

The temperature function of intercept, g(T), adjusts the intercept ofthe correlation for the reference temperature to the intercept of acorrelation for another temperature. The temperature-adjusted interceptmay be used to calculate the analyte or glucose concentration using anoutput signal or current generated at the other temperature. To developthe temperature function of intercept, g(T), the intercepts ofcorrelations for different temperatures are normalized to the interceptof the correlation for the reference temperature. The normalizedintercept of a correlation for a particular temperature is a unitlesscoefficient that adjusts the intercept of the correlation for thereference temperature to the intercept of the correlation for theparticular temperature. The normalized intercept of the correlation forthe reference temperature is essentially one, indicating there is littleor no adjustment to the intercept of the correlation for the referencetemperature. The normalized intercepts are analyzed graphically and/ormathematically such as with a regression analysis to develop thetemperature function of intercept, g(T). Another normalization methodmay be used to develop the temperature function.

The temperature function of intercept, g(T), may be a second orderpolynomial such as follows:g(T)=b ₂ T ² +b ₁ T+b ₀  (10).

Where T is the sample temperature and b₂, b₁, and b₀ are coefficients ofa regression analysis representing the normalized intercepts. Whilerepresented as a polynomial, the temperature function of intercept,g(T), may be represented as a constant, an exponential, trigonometric,or other function, a combination thereof, and the like.

In 108 of FIG. 1, the analyte concentration of the sample is determinedfrom the temperature-adjusted correlation equation (6) and the outputsignal at the sample temperature. The temperature functions of slope andintercept, f(T) and g(T), are calculated using equations (8) and (10),respectively. S_(T) and Int_(T), the slope and intercept of thecorrelation for the reference temperature adjusted in response to thesample temperature, are calculated using equations (7) and (9),respectively.

In 110 of FIG. 1, the analyte concentration calculated usingtemperature-adjusted correlation equation (6) and the output signal atthe sample temperature may be displayed or stored for future reference.

The effect of changes in the slope and intercept on analyteconcentration in relation to temperature changes may be analyzed.Temperature coefficients define the change in a parameter in relation tothe change in temperature. For parameters such as analyte concentration,slope, and intercept, temperature coefficients may be defined asfollows:

$\begin{matrix}{\alpha_{A} = {\frac{{\partial A}/A}{\partial T} = {\frac{\Delta\;{A/A}}{\Delta\; T}.}}} & (11) \\{\alpha_{S} = {\frac{{\partial S}/S}{\partial T} = {\frac{\Delta\;{S/S}}{\Delta\; T}.}}} & (12) \\{\alpha_{Int} = {\frac{{\partial{Int}}/{Int}}{\partial T} = {\frac{\Delta\;{{Int}/{Int}}}{\Delta\; T}.}}} & (13)\end{matrix}$

Where α_(A), α_(s), and α_(Int) are the temperature coefficients of theanalyte concentration, slope, and intercept respectively, A is theanalyte concentration, S is the slope, Int is the intercept, and T istemperature.

For a constant input signal such as current, the relative change in theanalyte concentration, A, in relation to changes in the slope, S, andintercept, Int, may be given as follows using the analyte calculationequation (6) as follows:

$\begin{matrix}{{dA} = {{\frac{\partial A}{\partial S}{dS}} + {\frac{\partial A}{\partial{Int}}{{d{Int}}.}}}} & (14) \\{\frac{dA}{A} = {\left\lbrack {{\frac{\partial A}{\partial S}{dS}} + {\frac{\partial A}{\partial{Int}}{d{Int}}}} \right\rbrack/{A.}}} & (15) \\{\frac{\partial A}{\partial S} = {{\frac{{OS} - {Int}}{S}\left( {{- 1}/S} \right)} = {- {\frac{A}{S}.}}}} & (16) \\{\frac{\partial A}{\partial{Int}} = {{- 1}/{S.}}} & (17)\end{matrix}$

Where OS is an output signal such as current.

Substituting equations (16) and (17) into equation (15), gives thefollowing relationships for the relative change in an analyteconcentration such as glucose:

$\begin{matrix}{\frac{dA}{A} = {{- \frac{dS}{S}} - {\frac{d{Int}}{\left( {S*A} \right)}.}}} & (18) \\{\frac{\Delta\; A}{A} = {{{- \frac{\Delta\; S}{S}} - \frac{\Delta\;{Int}}{\left( {S*A} \right)}} = {{- \frac{\Delta\; S}{S}} - {\left\lbrack \frac{{Int}/S}{A} \right\rbrack*{\left\lbrack \frac{\Delta\;{Int}}{Int} \right\rbrack.}}}}} & (19)\end{matrix}$

Substituting the temperature coefficients from equations (11), (12), and(13) and translating equation (19) provides the following relationships:

$\begin{matrix}{\frac{\Delta\;{A/A}}{\Delta\; T} = {{- \frac{\Delta\;{S/S}}{\Delta\; T}} - {\left\lbrack \frac{{Int}/S}{A} \right\rbrack*{\left\lbrack \frac{{\Delta{Int}}/{Int}}{\Delta\; T} \right\rbrack.}}}} & (20) \\{\frac{\Delta\;{A/A}}{\Delta\; T} = {\alpha_{A} = {{- \alpha_{S}} - {\left\lbrack \frac{{Int}/S}{A} \right\rbrack*{\alpha_{int}.}}}}} & (21)\end{matrix}$

Equation (21) indicates that the effect of the temperature coefficientof slope is equivalent to the analyte concentration, but is opposite inmagnitude. However, the effect of the temperature coefficient ofintercept may be smaller in magnitude, depending on the slope,intercept, and analyte concentration being measured.

For an analyte such as glucose in whole blood, the effect of changes inthe intercept temperature coefficient on the glucose temperaturecoefficient is small at higher glucose concentrations. If the ratio ofintercept to slope, Int/S, is 50 and the glucose concentration is 150mg/dL, only one-third of the intercept temperature coefficient has aneffect on the glucose temperature coefficient (the effect of temperatureon the temperature coefficient of the glucose concentration includesonly one-third of the effect of temperature on the temperaturecoefficient of the intercept). At lower glucose concentrations, theeffect of the intercept temperature coefficient on the glucosetemperature coefficient is more visible. If the ratio of intercept toslope, Int/S, is 50 and the glucose concentration is 50 mg/dL, all ofthe intercept temperature coefficient has an effect on the glucosetemperature coefficient (the effect of temperature on the temperaturecoefficient of the glucose concentration includes all of the effect oftemperature on the temperature coefficient of the intercept). A smallerInt/S ratio reduces the effect of intercept temperature coefficient onthe glucose temperature coefficient.

FIG. 2 represents a method for adjusting a correlation between analyteconcentrations and output signals at a reference temperature in responseto temperature. In 202, the correlations between analyte concentrationsand output signals are determined for a reference temperature and atleast one other temperature. In 204, normalized temperature functionsare developed of slope and intercept for the correlation of thereference temperature. In 206, the correlation of the referencetemperature is adjusted in response to the normalized temperaturefunctions of slope and intercept. This method may be used with themethod described in relation to FIG. 1, a similar method, or otherwise.

In 202 of FIG. 2, correlations between analyte concentrations and outputsignals are determined for a reference temperature and at least oneother temperature. The output signals may be generated by anelectrochemical reaction of the analyte in the sample as previouslydiscussed. For each temperature, output signals are generatedexperimentally by electrochemical reactions at different analyteconcentrations. The experimental results are analyzed to develop acorrelation between the analyte concentrations and the output signalsfor each temperature.

FIG. 3 is a graph illustrating correlations between analyteconcentrations and output signals. In this illustration, each outputsignal is the current generated from an electrochemical reaction, suchas gated amperometry. The analyte concentrations are glucoseconcentrations in whole blood. Correlations between current and glucoseconcentrations are graphically shown for a reference temperature of 25°C. and two other temperatures—10° C. and 40° C. While the correlation at25° C. was selected as the reference temperature, correlations at othertemperatures (including those not shown) may be selected as thereference temperature. While the illustration is directed towardparticular features, such as the number of correlations, output signals,analyte concentrations, temperatures, and the like, the illustration isnot meant to limit the scope, application, implementation, or the like.

Each of the graphical correlations is linear and may be represented by acorrelation equation having a general form as follows:

$\begin{matrix}{G = {\frac{I - {Int}}{S}.}} & (22)\end{matrix}$

Where G is the glucose concentration, I is the current, Int is theintercept of the correlation line with the y-axis, and S is the slope ofthe correlation line. While linear relationships are shown for thecorrelations between the glucose concentration and the current, othercorrelations may have other relationships, such as polynomial,exponential, trigonometric, a combination thereof, and the like.

In 204 of FIG. 2, normalized temperature functions are developed ofslope and intercept for the correlation of the reference temperature.The temperature functions adjust the slope and intercept of thecorrelation for the reference temperature to the slope and intercept ofa correlation for another temperature. The temperature-adjusted slopeand intercept may be used to calculate the analyte or glucoseconcentration using an output signal or current generated at the othertemperature.

To develop the temperature functions, the slopes and intercepts arenormalized to the slope and intercept of the correlation for thereference temperature. The normalized slope of a correlation for aparticular temperature is a unitless coefficient that adjusts the slopeof the correlation for the reference temperature to the slope of thecorrelation for the particular temperature. The normalized intercept ofa correlation for a particular temperature is a unitless coefficientthat adjusts the intercept of the correlation for the referencetemperature to the intercept of the correlation for the particulartemperature. Both the normalized slope and normalized intercept of thecorrelation for the reference temperature are essentially one,indicating there is little or no adjustment to the slope and interceptof the correlation for the reference temperature. Other normalizationmethods may be used.

The normalized slopes of the correlations may be used to generate atemperature function of the slope, f(T), graphically and/ormathematically using a regression analysis or the like. The temperaturefunction of the slope, f(T), from a regression analysis may be a secondorder polynomial such as follows:f(T)=a ₂ T ² +a ₁ T+a ₀  (23).

Where T is the sample temperature and a₂, a₁, and a₀ are coefficients ofa regression analysis representing the normalized slopes. Whilerepresented as a polynomial, the regression analysis may represent thetemperature function of the slope, f(T), as another function.

The normalized intercepts of the correlations may be used to generate atemperature function of the intercept, g(T), graphically and/ormathematically using a regression analysis or the like. The temperaturefunction of the intercept, g(T), from a regression analysis may be asecond order polynomial such as follows:g(T)=b ₂ T ² +b ₁ T+b ₀  (24).

Where T is the sample temperature and b₂, b₁, and b₀ are coefficients ofa regression analysis representing the normalized intercepts. Whilerepresented as a polynomial, the regression analysis may represent thetemperature function of the intercept, g(T), as another function.

FIG. 3 illustrates that correlations between current and glucose at 10°C., 25° C., and 40° C. calculate the same glucose concentration, G₂₅,from currents, i₄₀, i₂₅, and i₁₀, which are generated by electrochemicalreactions of the analyte in the sample at those respective temperatures.The slopes and intercepts of the correlations may be normalized to theslope and intercept of the correlation for the reference temperature of25° C. The normalized slopes and intercepts of the correlations may beused to generate the temperature function of the slope, f(T), and thetemperature function of the intercept, g(T).

FIGS. 4 and 5 are graphs illustrating the normalized slopes andintercepts, respectively, as a function of temperature for correlationsbetween glucose concentrations in whole blood and current. Thecorrelations were generated from electrochemical reactions using gatedamperometry with an assay time of 7 seconds (sec). The normalized slopesand intercepts are from correlations at 10° C., 20° C., 25° C., 30° C.,and 40° C. The normalized slopes and intercepts were normalized to theslope and intercept of a correlation at a reference temperature of 25°C. While these illustrations are directed toward particular featuressuch as normalized slopes, temperatures, and the like, the illustrationsare not meant to limit the scope, application, implementation, or thelike.

In FIG. 4, a regression analysis of the normalized slopes generates atemperature function of the slope, f(T), as follows:f(T)=−0.00005765*T ²+0.01453*T+0.6703  (25).

The temperature function of the slope, f(T), shown in equation (25) maybe used to adjust the slope of the correlation for the referencetemperature of 25° C. to the slope of a correlation for anothertemperature, such as a sample temperature. T is the other temperature.The temperature-adjusted slope may be used to calculate the glucoseconcentration using a current generated at the other temperature. Othertemperature functions of the slope may be used.

In FIG. 5, a regression analysis of the normalized intercepts generatesa temperature function of the intercept, g(T), as follows:g(T)=0.0001023*T ²+0.01389*T+1.284  (26).

The temperature function of the intercept, g(T), shown in equation (26)may be used to adjust the intercept of the correlation for the referencetemperature of 25° C. to the intercept of a correlation for anothertemperature, such as a sample temperature. T is the other temperature.The temperature-adjusted intercept may be used to calculate the glucoseconcentration using a current generated at the other temperature. Othertemperature functions for the intercept may be used.

The separate temperature functions for slope and intercept may be usedwith a program number assignment (PNA) table of the slope and interceptof the correlation for the reference temperature. In addition, thenormalized slope and intercept provide a range in which the intrinsictemperature properties of a biosensor system may be independent of theoutput signal or current magnitude generated by the electrochemicalreaction. The intrinsic temperature properties usually depend on thesensor strip design and manufacturing. A biosensor system may change thetemperature functions and/or correlation equation (s) in response to thesensor strip type and batch used. The temperature function andcorrelation equation changes may be made by changing PNA table when adifferent or new sensor strip is used.

FIGS. 6 and 7 are graphs illustrating the normalized slopes andintercepts, respectively, as a function of temperature for correlationsbetween glucose concentrations in whole blood and current. Thecorrelations were generated from electrochemical reactions using gatedamperometry with assay times of 5.5 sec, 7 sec, 8.5 sec, 10 sec, 11.5sec, 13 sec, and 14.5 sec. The normalized slopes and intercepts are fromcorrelations at 10° C., 20° C., 25° C., 30° C., and 40° C. Thenormalized slopes and intercepts were normalized to the slope andintercept of a correlation at a reference temperature of 25° C. Whilethese illustrations are directed toward particular features, such asnormalized slopes, temperatures, and the like, the illustrations are notmeant to limit the scope, application, implementation, or the like.

FIGS. 6 and 7 illustrate normalized slopes and intercepts forelectrochemical reactions using gated amperometry with multiple assaytimes. In determining temperature functions for normalized slopes andintercepts in electrochemical methods based on multiple pulses, thereare multiple calibration points in the individual pulses of a pulsesequence. By using currents generated at different temperatures anddifferent times in different pulses, slopes and intercepts from thedifferent temperatures can be normalized to the slope and intercept at25° C. The normalized slopes and intercepts may be representedgraphically and/or mathematically as a function of temperature. Themathematical representation may be by a regression analysis thatgenerates a second order polynomial. In multiple pulse methods, theremay be many calibration points in a time range such as from 5.5 sec. to7, 8.5, and 10 sec. Within this range, the intrinsic temperatureproperty of a biosensor should be consistent if the reagents aresufficiently hydrated.

In FIG. 6, the temperature functions of the normalized slopesessentially overlap each other except for the 5.5 sec. assay time, whichreflects the intrinsic consistency of the temperature sensitivity of thebiosensor system. In addition, the temperature functions of thenormalized slopes are quite symmetrical with respect to the referencetemperature of 25° C. The normalized slopes at 10° C. are about 20%smaller than the normalized slope at 25° C. The normalized slopes at 40°C. are about 20% larger than the normalized slope at 25° C.

In FIG. 7, the temperature functions for normalized intercepts are verysimilar for assay times between 5.5 sec. and 10 sec. At longer times,the temperature effect on the normalized intercept becomes larger.

In 206 of FIG. 2, the correlation of the reference temperature isadjusted in response to the normalized temperature functions of slopeand intercept. The correlation between analyte concentrations and outputsignals for the reference temperature is as follows:

$\begin{matrix}{G_{R} = {\frac{i_{R} - {Int}_{R}}{S_{R}}.}} & (27)\end{matrix}$

Where G_(R) is the analyte concentration at the reference temperature,i_(R) is the output signal at the reference temperature, Int_(R) is theintercept of the correlation for the reference temperature, and S_(R) isthe slope of the correlation for the reference temperature.

The correlation for the reference temperature represented by equation(27) may be adjusted in response to a sample temperature. Analyteconcentrations at the reference temperature may be calculated usingtemperature-adjusted slopes and intercepts of the correlation for thereference temperature and output signals at a sample temperature, asfollows:

$\begin{matrix}{G_{R} = {\frac{i_{T} - {Int}_{T}}{S_{T}}.}} & (28)\end{matrix}$

Where G_(R) is the analyte concentration at the reference temperature,i_(T) is the output signal at the sample temperature, Int_(T) is theintercept of the correlation for the reference temperature adjusted inresponse to the sample temperature, and S_(T) is the slope of thecorrelation for the reference temperature adjusted for the sampletemperature.

The slope of the correlation for the reference temperature adjusted inresponse to the sample temperature, S_(T), may be calculated as follows:S _(T) =S _(R) *f(T)  (29).

Where S_(R) is the slope of the correlation for the referencetemperature and f(T) is a temperature function that adjusts the slopefor the sample temperature.

The intercept of the correlation for the reference temperature adjustedin response to the sample temperature, Int_(T), may be calculated asfollows:Int _(T) =Int _(T) *g(T)  (30).

Where Int_(R) is the intercept of the correlation for the referencetemperature and g(T) is a temperature function that adjusts theintercept for the sample temperature.

The correlation for the reference temperature adjusted in response to asample temperature as represented by equation (28) may be rewritten bysubstituting equations (29) and (30) for S_(T) and Int_(T), as follows:

$\begin{matrix}{G_{R} = {\frac{i_{T} - \left( {{Int}_{R}*{g(T)}} \right)}{\left( {S_{R}*{f(T)}} \right)}.}} & (31)\end{matrix}$

Where G_(R) is the analyte concentration at the reference temperature,i_(T) is the output signal at the sample temperature, Int_(R) is theintercept for the correlation of the reference temperature, g(T) is thenormalized temperature function for intercept, S_(R) is the slope forthe correlation of the reference temperature, and f(T) is the normalizedtemperature function for slope.

The correlation for the reference temperature adjusted in response to asample temperature as represented by equation (31) may be rewritten foruse with the examples illustrated in FIGS. 3-5, as follows:

$\begin{matrix}{G_{25} = {\frac{i_{T} - \left( {{Int}_{25}*\left( {{{- 0.00005765}*T^{2}} + {0.01453*T} + 0.6703} \right)} \right)}{\left( {S_{25}*\left( {{0.0001023*T^{2}} + {0.01389*T} + 1.284} \right)} \right)}.}} & (32)\end{matrix}$

Where G₂₅ is the analyte concentration at the reference temperature of25° C., i_(T) is the output signal at the sample temperature, Int₂₅ isthe intercept of the correlation for the reference temperature of 25°C., S₂₅ is the slope of the correlation for the reference temperature of25° C., and T is the sample temperature.

FIGS. 8 and 9 are graphs illustrating the glucose bias values from areference temperature as a function of temperature. FIG. 8 is a graphillustrating the bias of calculated glucose concentrations without anyadjustment for temperature. FIG. 9 is a graph illustrating the bias ofcalculated glucose concentrations with adjustment for temperature asdescribed previously. These graphs illustrate the percent bias from areference temperature of 25° C. for plasma glucose concentrations of56.9 mg/dL, 114.0 mg/dL, and 432.9 mg/dL in whole blood. The analysiswas generated from electrochemical reactions using gated amperometrywith an assay time of 7 sec at sample temperatures of 10° C., 20° C.,25° C., 30° C., and 40° C. While the illustrations are directed towardparticular features such as temperatures, glucose concentrations, andthe like, the illustrations are not meant to limit the scope,application, implementation, or the like.

In FIGS. 8 and 9, the percent bias values at 10° C., 20° C., and 25° C.for the 56.9 mg/dL glucose concentration show little if any change afterthe temperature adjustment, especially the percent bias value at 10° C.FIG. 8 indicates that the glucose concentrations from a correlationwithout temperature compensation generally have a negative bias attemperatures below the reference temperature of 25° C. FIG. 8 alsoindicates that glucose concentrations from a correlation withouttemperature adjustment generally have a positive bias at temperaturesabove the reference temperature of 25° C. FIG. 9 indicates that thepercent bias values converge to a narrower range of about +/−5 percentwhen correlations with the temperature adjustment are used.

The temperature coefficient function of any particular parameter may beused to further show the internal consistency of the temperaturefunction for adjusting correlation equations between analyteconcentrations and output signals. The temperature coefficient (theintrinsic property) of the output signal, OS, may be defined as follows:

$\begin{matrix}{\alpha_{OS} = {\frac{{\partial{OS}}/{OS}}{\partial T} = {\frac{\partial{\ln({OS})}}{\partial T}.}}} & (33)\end{matrix}$

Where α_(OS), is the temperature coefficient of the output signal, OS isthe output signal, and T is temperature.

FIGS. 10 and 11 are graphs illustrating the effect on the temperaturecoefficient function of the temperature-adjusted correlation equationsbetween analyte concentrations and output signals. FIG. 10 illustratesthe temperature function of current from a glucose sensor withnormalized slope and intercept. FIG. 11 illustrates the temperaturecoefficient function for the normalized current of FIG. 10 in relationto temperature. The normalized current and temperature coefficients(TempCo) are in response to glucose concentrations of 50 mg/dL, 100mg/dL, 200 mg/dL, 400 mg/dL, and 600 mg/dL. In FIG. 10, the current at25° C. should be equal to the glucose value according to equation (5)for the normalized slope and intercept. FIG. 11 indicates that thetemperature coefficients are functions of temperature—the lower thetemperature, the higher the temperature coefficient. Within thetemperature range of about 10° C. through about 40° C., the temperaturecoefficient ranges from about 1.85%/° C. through about 0.75%/° C. Inaddition, the temperature coefficient functions are independent ofglucose concentration. While the illustrations are directed towardparticular features such as temperature, glucose concentrations, and thelike, the illustrations are not meant to limit the scope, application,implementation, or the like.

FIG. 12 depicts a schematic representation of a biosensor 1200 thatdetermines an analyte concentration in a sample of a biological fluid.Biosensor 1200 includes a measuring device 1202 and a sensor strip 1204,which may be implemented as a bench-top device, a portable or hand-helddevice, or the like. The measuring device 1202 and the sensor strip 1204may be adapted to implement an electrochemical sensor system, an opticalsensor system, a combination thereof, or the like. The biosensor 1200adjusts a correlation for determining analyte concentrations from outputsignals at one temperature to determining analyte concentrations fromoutput signals at other temperatures, such as a sample temperature aspreviously discussed. The temperature-adjusted correlations improve theaccuracy and precision of the biosensor 1200 in determining the analyteconcentration of the sample. The biosensor 1200 may be utilized todetermine analyte concentrations, including those of glucose, uric acid,lactate, cholesterol, bilirubin, and the like. While a particularconfiguration is shown, the biosensor 1200 may have otherconfigurations, including those with additional components.

The sensor strip 1204 has a base 1206 that forms a reservoir 1208 and achannel 1210 with an opening 1212. The reservoir 1208 and the channel1210 may be covered by a lid with a vent. The reservoir 1208 defines apartially-enclosed volume (the cap-gap). The reservoir 1208 may containa composition that assists in retaining a liquid sample such aswater-swellable polymers or porous polymer matrices. Reagents may bedeposited in the reservoir 1208 and/or channel 1210. The reagents mayinclude one or more enzymes, binders, mediators, and like species. Thereagents may include a chemical indicator for an optical system. Thesensor strip 1204 also may have a sample interface 1214 disposedadjacent to the reservoir 1208. The sample interface 1214 may partiallyor completely surround the reservoir 1208. The sensor strip 1204 mayhave other configurations.

In an optical sensor system, the sample interface 1214 has an opticalportal or aperture for viewing the sample. The optical portal may becovered by an essentially transparent material. The sample interface mayhave optical portals on opposite sides of the reservoir 1208.

In an electrochemical system, the sample interface 1214 has conductorsconnected to a working electrode and a counter electrode. The electrodesmay be substantially in the same plane. The electrodes may be separatedby greater than 200 or 250 μm and may be separated from the lid by atleast 100 μm. The electrodes may be disposed on a surface of the base1206 that forms the reservoir 1208. The electrodes may extend or projectinto the cap-gap formed by the reservoir 1208. A dielectric layer maypartially cover the conductors and/or the electrodes. The sampleinterface 1214 may have other electrodes and conductors.

The measuring device 1202 includes electrical circuitry 1216 connectedto a sensor interface 1218 and a display 1220. The electrical circuitry1216 includes a processor 1222 connected to a signal generator 1224, atemperature sensor 1226, and a storage medium 1228.

The signal generator 1224 provides an electrical input signal to thesensor interface 1218 in response to the processor 1222. In opticalsystems, the electrical input signal may be used to operate or controlthe detector and light source in the sensor interface 1218. Inelectrochemical systems, the electrical input signal may be transmittedby the sensor interface 1218 to the sample interface 1214 to apply theelectrical input signal to the sample of the biological fluid. Theelectrical input signal may be a potential or current and may beconstant, variable, or a combination thereof, such as when an AC signalis applied with a DC signal offset. The electrical input signal may beapplied as a single pulse or in multiple pulses, sequences, or cycles.The signal generator 1224 also may record an output signal from thesensor interface as a generator-recorder.

The temperature sensor 1226 determines the temperature of the sample inthe reservoir of the sensor strip 1204. The temperature of the samplemay be measured, calculated from the output signal, or assumed to be thesame or similar to a measurement of the ambient temperature or thetemperature of a device implementing the biosensor system. Thetemperature may be measured using a thermister, thermometer, or othertemperature sensing device. Other techniques may be used to determinethe sample temperature.

The storage medium 1228 may be a magnetic, optical, or semiconductormemory, another computer readable storage device, or the like. Thestorage medium 1228 may be a fixed memory device or a removable memorydevice such as a memory card.

The processor 1222 implements the analyte analysis and data treatmentusing computer readable software code and data stored in the storagemedium 1228. The processor 1222 may start the analyte analysis inresponse to the presence of sensor strip 1204 at the sensor interface1218, the application of a sample to the sensor strip 1204, in responseto user input, or the like. The processor 1222 directs the signalgenerator 1224 to provide the electrical input signal to the sensorinterface 1218. The processor 1222 receives the sample temperature fromthe temperature sensor 1226. The processor 1222 receives the outputsignal from the sensor interface 1218. The output signal is generated inresponse to the redox reaction of the analyte in the sample. The outputsignal may be generated using an optical system, an electrochemicalsystem, or the like. The processor 1222 determines analyteconcentrations from output signals at a sample temperature using atemperature-adjusted correlation equation for a reference temperature aspreviously discussed. The results of the analyte analysis are output tothe display 1220 and may be stored in the storage medium 1228.

The correlation equations between analyte concentrations and outputsignals may be represented graphically, mathematically, a combinationthereof, or the like. The correlation equations may be represented by aprogram number (PNA) table, another look-up table, or the like that isstored in the storage medium 1228. Instructions regarding implementationof the analyte analysis may be provided by the computer readablesoftware code stored in the storage medium 1228. The code may be objectcode or any other code describing or controlling the functionalitydescribed herein. The data from the analyte analysis may be subjected toone or more data treatments, including the determination of decay rates,K constants, slopes, intercepts, and/or sample temperature in theprocessor 1222.

In electrochemical systems, the sensor interface 1218 has contacts thatconnect or electrically communicate with the conductors in the sampleinterface 1214 of the sensor strip 1204. The sensor interface 1218transmits the electrical input signal from the signal generator 1224through the contacts to the connectors in the sample interface 1214. Thesensor interface 1218 also transmits the output signal from the samplethrough the contacts to the processor 1222 and/or signal generator 1224.

In light-absorption and light-generated optical systems, the sensorinterface 1218 includes a detector that collects and measures light. Thedetector receives light from the liquid sensor through the opticalportal in the sample interface 1214. In a light-absorption opticalsystem, the sensor interface 1218 also includes a light source such as alaser, a light emitting diode, or the like. The incident beam may have awavelength selected for absorption by the reaction product. The sensorinterface 1218 directs an incident beam from the light source throughthe optical portal in the sample interface 1214. The detector may bepositioned at an angle such as 45° to the optical portal to receive thelight reflected back from the sample. The detector may be positionedadjacent to an optical portal on the other side of the sample from thelight source to receive light transmitted through the sample.

The display 1220 may be analog or digital. The display may be an LCDdisplay adapted to displaying a numerical reading.

In use, a liquid sample for analysis is transferred into the cap-gapformed by the reservoir 1208 by introducing the liquid to the opening1212. The liquid sample flows through the channel 1210 into thereservoir 1208, filling the cap-gap while expelling the previouslycontained air. The liquid sample chemically reacts with the reagentsdeposited in the channel 1210 and/or reservoir 1208.

The sensor strip 1204 is disposed adjacent to the measuring device 1202.Adjacent includes positions where the sample interface 1214 is inelectrical and/or optical communication with the sensor interface 1218.Electrical communication includes the transfer of input and/or outputsignals between contacts in the sensor interface 1218 and conductors inthe sample interface 1214. Optical communication includes the transferof light between an optical portal in the sample interface 1214 and adetector in the sensor interface 1218. Optical communication alsoincludes the transfer of light between an optical portal in the sampleinterface 1214 and a light source in the sensor interface 1218.

The processor 1222 receives the sample temperature from the temperaturesensor 1226. The processor 1222 directs the signal generator 1224 toprovide an input signal to the sensor interface 1218. In an opticalsystem, the sensor interface 1218 operates the detector and light sourcein response to the input signal. In an electrochemical system, thesensor interface 1218 provides the input signal to the sample throughthe sample interface 1214. The processor 1222 receives the output signalgenerated in response to the redox reaction of the analyte in the sampleas previously discussed.

The processor 1222 determines the analyte concentration of the sample.The measuring device adjusts the correlation between analyteconcentrations and output signals at a reference temperature in responseto the sample temperature. The analyte concentration is determined fromthe temperature-adjusted correlation and the output signal at the sampletemperature. In 110, the analyte concentration is displayed and may bestored for future reference.

Without limiting the scope, application, or implementation, the methodsand systems previously described may be implemented using the followingalgorithm:

Step 1: Turn on meter power

Step 2: Perform biosensor Self-test

Step 3: Perform standardization of biosensor electronics

Step 4: Measure temperature, T

Step 5: Check temperature range

-   -   if (T>T_(Hi)) then, Set Error Mode, “Temperature too high”    -   if (T<T_(Low)) then, Set Error Mode, “Temperature too low”

Step 6: Apply input signal to sample

Step 7: Measure output signal, i

Step 8: Look up slope and intercept in program number assignment (PNA)table

-   -   S=Slope value for current    -   Int=Intercept for current

Step 9: Adjust slope and intercept for temperature effect.

-   -   S_(T)=S*(a₂*T₁ ²+a₁*T₁+a₀)    -   Int_(T)=Int*(b₂*T₁ ²+b₁*T₁+b₀)

Step 10: Calculate glucose concentration at 25° C.

$G_{25} = \frac{i_{T} - {Int}_{T}}{S_{T}}$

Step 11: Check for extreme glucose levels

-   -   if (G₂₅>G_(max)) then, Set Error Mode, “Glucose too high”

Step 12: Display result

A program number assignment (PNA) table that may be used in thealgorithm is given in Table I below. The constants that may be used inthe algorithm are given in Table II below. Other PNA tables and/orconstants may be used.

TABLE I slope of slope of slope of slope of column column column columncode 8.028 code 8.498 code 8.995 code 9.522 PNA # table # intercept PNA# table # intercept PNA # table # intercept PNA # table # intercept 1 1310.04 18 18 310.62 34 35 311.24 49 52 311.90 2 2 330.11 19 19 331.87 3536 333.73 50 53 335.71 3 3 350.18 20 20 353.11 36 37 356.22 51 54 359.514 4 370.25 21 21 374.36 37 38 378.71 52 55 383.32 5 5 390.32 22 22395.60 38 39 401.20 53 56 407.12 6 6 410.39 23 23 416.85 39 40 423.69 5457 430.92 7 7 430.46 24 24 438.09 40 41 446.17 55 58 454.73 8 8 450.5325 25 459.34 41 42 468.66 56 59 478.53 9 9 470.60 26 26 480.58 42 43491.15 57 60 502.34 10 10 490.67 27 27 501.83 43 44 513.64 58 61 526.1411 11 510.74 28 28 523.07 44 45 536.13 59 62 549.95 12 12 530.81 29 29544.32 45 46 558.62 60 63 573.75 13 13 550.88 30 30 565.56 46 47 581.1161 64 597.56 14 14 570.95 31 31 586.81 47 48 603.59 62 65 621.36 15 15591.02 32 32 608.05 48 49 626.08 66 16 16 611.09 33 33 629.30 50 67 1717 631.16 34 51 68

TABLE II CONSTANT DESCRIPTION VALUE UNITS T_(HI) Invalid TemperatureHigh 50 ° C. T_(LO) Invalid Temperature Low 5 ° C. a₂ coefficient, slopetemperature −5.765e−5 — function a₁ coefficient, slope temperature0.01453 — function a₀ coefficient, slope temperature 0.6703 — functionb₂ coefficient, intercept temperature 1.023 — function b₁ coefficient,intercept temperature −0.01389 — function b₀ coefficient, intercepttemperature 1.284 — function G_(max) maximum allowable glucose 1500mg/dL concentration

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that other embodimentsand implementations are possible within the scope of the invention.

What is claimed is:
 1. A method for determining an analyte concentration in a sample of a biological fluid, comprising: determining a sample temperature; generating an output signal in response to a redox reaction of an analyte in the sample at a sample temperature; selecting a previously determined correlation between output signals and analyte concentrations for a reference temperature; selecting a previously developed normalized temperature function, the development of the normalized temperature function comprising: determining a correlation between output signals and analyte concentrations for at least one other temperature; and normalizing the correlation at the at least one other temperature to the correlation of the reference temperature; adjusting the previously determined correlation with the previously developed normalized temperature function, to obtain a temperature-adjusted correlation; and calculating an analyte concentration from the output signal and the temperature-adjusted correlation.
 2. The method of claim 1, where the temperature-adjusted correlation is represented as follows: A=c ₂ *OS ² +c ₁ *OS+c ₀ where A is the analyte concentration; OS is the output signal; and c₂, c₁, and c₀ are coefficients that describe a temperature dependent weighing factor.
 3. The method of claim 1, where the temperature-adjusted correlation is represented as follows: OS _(T) =S _(T) *A _(R) +Int _(t) where OS_(T) is the output signal at the sample temperature, A_(R) is the analyte concentration at the reference temperature, S_(T) is a product of a slope at the reference temperature and a normalized temperature function of the slope, and Int_(t) is a product of an intercept at the reference temperature and a normalized temperature function of the intercept.
 4. The method of claim 3, where S_(T) is represented as follows: S _(T) =S _(R) *f(T) where T is the sample temperature, S_(R) is the slope of the correlation for the reference temperature, and f(T) is a temperature function that adjusts the slope for the sample temperature.
 5. The method of claim 4, where f(T) is represented as follows: f(T)=a ₂ T ² +a ₁ T+a₀ where T is the sample temperature, and a₂, a_(l), and a₀ are coefficients of a regression analysis representing normalized slopes.
 6. The method of claim 3, where Int_(T) is represented as follows: Int _(T) =Int _(R) *g(T) where T is the sample temperature, Int_(R) is the intercept of the correlation for the reference temperature, and g(T) is a temperature function that adjusts the intercept for the sample temperature.
 7. The method of claim 6, where g(T) is represented as follows: g(T)=b ₂ T ² +b ₁ T+b _(0,) where T is the sample temperature, and b₂, b₁, and b₀ are coefficients of a regression analysis representing normalized intercepts.
 8. The method of claim 1, further comprising generating the output signal in response to an electrochemical process.
 9. The method of claim 1, where the output signal comprises light.
 10. The method of claim 1, where the output signal comprises an electric signal.
 11. The method of claim 1, further comprising generating the output signal in response to pulsed input signals.
 12. A biosensor for determining an analyte concentration in a biological fluid, comprising: a measuring device having a processor connected to a sensor interface and a temperature sensor; a sensor strip having a sample interface on a base, where the sample interface is adjacent to a reservoir formed by the base; where the processor: selects a previously determined correlation between output signals and analyte concentrations for a reference temperature; selects a previously developed normalized temperature function, the development of the normalized temperature function comprising: determining a correlation between output signals and analyte concentrations for at least one other temperature; and normalizing the correlation at the at least one other temperature to the correlation of the reference temperature; adjusts the previously determined correlation with the previously developed normalized temperature function, to obtain a temperature-adjusted correlation adjusted to a sample temperature from the temperature sensor; and determines an analyte concentration from the temperature-adjusted correlation in response to an output signal from the sample interface.
 13. The biosensor of claim 12, where the temperature-adjusted correlation is represented as follows: A=c ₂ *OS ² +c ₁ *OS+c ₀ where A is the analyte concentration; OS is the output signal; and c₂, c₁, and c₀ are coefficients that describe a temperature dependent weighing factor.
 14. The biosensor of claim 12, where the temperature-adjusted correlation is represented as follows: OS _(T) =S _(T) *A _(R) +Int _(T) where OS_(T) is the output signal at the sample temperature, A_(R) is the analyte concentration at the reference temperature, S_(T) is a product of a slope at the reference temperature and a normalized temperature function of the slope, and Int_(T) is a product of an intercept at the reference temperature and a normalized temperature function of the intercept.
 15. The biosensor of claim 14, where S_(T) is represented as follows: S _(T) =S _(R) *f(T) where T is the sample temperature, S_(R) is the slope of the correlation for the reference temperature, and f(_(T)) is a temperature function that adjusts the slope for the sample temperature.
 16. The biosensor of claim 15, where f(T) is represented as follows: f(T)=a ₂ T ² +a ₁ T+a ₀ where T is the sample temperature, and a₂, a₁, and a₀ are coefficients of a regression analysis representing normalized slopes.
 17. The biosensor of claim 14, where Int_(T) is represented as follows: Int _(T) =Int _(R) *g(T) where T is the sample temperature, Int_(R) is the intercept of the correlation for the reference temperature, and g(T) is a temperature function that adjusts the intercept for the sample temperature.
 18. The biosensor of claim 17, where g(T) is represented as follows: g(T)=b ₂ T ² +b ₁ T+b ₀, where T is the sample temperature, and b₂, b₁, and b₀ are coefficients of a regression analysis representing normalized intercepts.
 19. A method for determining an analyte concentration in a sample of a biological fluid, comprising: applying the sample to the sensor strip of the biosensor of claim 12; determining a sample temperature; generating an output signal in response to a redox reaction of an analyte in the sample at the sample temperature; adjusting a correlation between analyte concentrations and output signals at a reference temperature in response to normalized functions of slope and intercept; and determining the analyte concentration from the temperature-adjusted correlation and the output signal at the sample temperature.
 20. The method of claim 19, where the output signal comprises light.
 21. The method of claim 19, where the output signal comprises an electrical signal.
 22. The method of claim 19, where the output signal is responsive to pulsed input signals.
 23. The method of claim 19, where the analyte comprises glucose and the biological fluid comprises whole blood. 